Abstract
Let F be an algebraic number field. The set of valuations on F is denoted by M F . Let |.| v , or v in shorthand, be a valuation of F. Denote by F v the completion of F with respect to v. If F v is ℝ or ℂ we assume that v coincides with the usual absolute value on these fields. When v is a finite valuation we assume it normalised by |p| v = 1/p where p is the unique rational prime such that |p| v < 1. The normalised valuation ‖.‖ v is defined by
with the convention that p = ∞ when v is archimedean and ℚ∞ = ℝ. For any non-zero x ∈ F we have the product formula
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© 1993 Springer-Verlag Berlin Heidelberg
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Beukers, F. (1993). Diophantine Equations and Approximation. In: Edixhoven, B., Evertse, JH. (eds) Diophantine Approximation and Abelian Varieties. Lecture Notes in Mathematics, vol 1566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48208-6_1
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DOI: https://doi.org/10.1007/978-3-540-48208-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57528-3
Online ISBN: 978-3-540-48208-6
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